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THROUGH FINLAND. 381
‘¢ differ fenfibly from that of a fphere, the equation x =o will
*‘ neceffarily contain one or more of thofe {mall quantities a, b,
« &e fo affected, that if we fuppofe them = 0, the remaining
ee equation z = 0 will be that of a fphere, whofe dimenfions are
*‘ equal to thofe of the earth; whence it will follow that z will
«be the firft term of our developed feries, as we have juft faid.
* Befides, if we except aA, and 2Ao.1, all the other terms
cog bh A may be difregarded on account of the fmallnefs of
M2
“the quantities a, b, &c.; confequently the furfaee of our globe
“ will be reprefented by the equation U x an, * bAy, ==) Os
“«¢ The whole then comes to this, to know what is the form of
“the functions A, , and Ay, which being fuppofed of the fe-
“cond order, the equation z= 0 will reprefent an ellipfoid,
‘‘ whofe eccentricities of the equator, and of the meridian which:
“¢ pafles through the great axis of the equator, will depend on the
‘ quantities a, b, &c. In refpect of the figure of revolution, it
‘‘ is very clear that then the quantity a will be nearly equal to 4,
** or what is the fame thing, if we make a = 0 x 6, the quan-
“ tity « will be very {mall ; whence it follows that the equation. -
‘4 = 0, may be reprefented by this o = U X bA, In fhort,
‘¢ there is no reafon to fear that the difregarded quantities fhould:
*‘ ever prove confiderable enough to produce any error of confe-
** quence, as difficulties which in all probability we fhall never be
“« able fully to furmount, will for ever prevent our precifely know-
singe
ai
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